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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fredholmness and invertibility of Toeplitz operators with matrix almost periodic symbols


Authors: Leiba Rodman, Ilya M. Spitkovsky and Hugo J. Woerdeman
Journal: Proc. Amer. Math. Soc. 130 (2002), 1365-1370
MSC (2000): Primary 47B35, 43A60
Published electronically: September 19, 2001
MathSciNet review: 1879958
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider Toeplitz operators with symbols that are almost periodic matrix functions of several variables. It is shown that under certain conditions on the group generated by the Fourier support of the symbol, a Toeplitz operator is Fredholm if and only if it is invertible.


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Additional Information

Leiba Rodman
Affiliation: Department of Mathematics, The College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795
Email: lxrodm@math.wm.edu

Ilya M. Spitkovsky
Affiliation: Department of Mathematics, The College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795
Email: ilya@math.wm.edu

Hugo J. Woerdeman
Affiliation: Department of Mathematics, The College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795
Email: hugo@math.wm.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06276-1
PII: S 0002-9939(01)06276-1
Keywords: Almost periodic functions, Toeplitz operators, Fredholmness
Received by editor(s): October 28, 2000
Published electronically: September 19, 2001
Additional Notes: The research of all three authors was partially supported by NSF grant DMS-9988579.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2001 American Mathematical Society